Quantifying the abundance and survival rates of island-associated spinner dolphins using a multi-state open robust design model

Spinner dolphins (Stenella longirostris subsp.) occupy the nearshore waters of several Hawaiian Islands. Due to their constrained behavioral pattern and genetic isolation, they are vulnerable to anthropogenic threats. Their occurrence and behavior are well-described, yet a lack of data on their abundance and survival rates hinders optimal conservation action. Using design-based photo-identification surveys, this study estimated the abundance, apparent survival, and emigration of spinner dolphins off the Waiʻanae Coast of Oʻahu through multi-state open robust design (MSORD) and POPAN modelling. Eight seasonal field seasons, (two winter, spring, summer, and autumn) each comprised of six surveys of the study area, were completed during two consecutive years. Seasonal abundance estimates derived from the best fitting model ranged from 140 (± 36.8 SE, 95% CI 84–232) to 373 (± 60.0, 95% CI 273–509) individuals and were lowest during winter seasons. The MSORD estimated a survival rate of 0.95 (± 0.02 SE) and a Markovian pattern of temporary emigration. POPAN modelling estimated a super-population size of 633 (± 78 SE, 95% CI 492–798), reflecting the total number of individual dolphins that used the study area during the entire study period. Additional research on circum- and inter-island dolphin movements around and between Oʻahu and the Maui Nui region may shed light on both seasonal movement patterns and overall abundance for the Oʻahu/4-Islands stock. This work represents the first systematic mark-recapture effort to assess the abundance and survival rates of these highly exposed dolphins, providing valuable insights for conservation and management.

Information on the abundance, survival, and movement patterns of wildlife populations is important to understand their conservation status 1 .Repeated estimates of population abundance can provide insights into a population's seasonal distribution 2,3 , trajectory 4,5 , and interactions with anthropogenic and environmental stressors 6,7 .Such knowledge is critical to informing data-driven conservation and management actions to protect vulnerable species 8,9 .
In the marine environment, apex predators such as cetaceans play crucial roles in maintaining ecological balance 10,11 and serve as indicator species for monitoring ecosystem health 12 .Moreover, cetaceans hold considerable economic and cultural value [13][14][15][16] , yet face a wide range of threats from human activity.Cetaceans are sensitive to anthropogenic disturbance such as direct and incidental removal 17 , habitat degradation 18 and human-induced behavioral change 6 .In remote island regions with high human density, anthropogenic impacts on cetaceans are of particular concern, as small island-associated populations often exhibit specialized behavior, low gene flow and high site fidelity [19][20][21] .
Island-associated spinner dolphins (Stenella longirostris subsp.) in Hawaiʻi exhibit rigid daily patterns of activity, socializing and resting in nearshore waters during the day, and moving offshore at night to feed on fish and

Model selection
The most parsimonious MSORD model based on selection by AICc score had Markovian emigration, constant apparent survival and capture probabilities, and entry and persistence probabilities that varied by season and day (Table 2).No other models were within 2 AICc units of the best scoring model, though many parameter estimates were similar between top ranking models.A one-way ANOVA test showed no significance for the influence of swell ( p = 0.39) and sea state ( p = 0.56) on the number of dolphin groups sighted in each season, indicating that constant capture probability was plausible.Both the global-GOF test ( c = 1.38 , χ 2 = 531 , df = 384 ) and pooled secondary period tests (TEST 2: c = 2.16 , χ 2 = 26 , df = 12 ; TEST 3: c = 2.09 , χ 2 = 23 , df = 11 ) indicated good fit for the underlying data.
For POPAN modelling, the GOF test for the CJS global model ( c = 2.13 , χ 2 = 49 , df = 23 ) indicated overd- ispersion of the data.To reduce overdispersion, the models were adjusted by c and ranked by QAICc score.The most parsimonious POPAN model had time varying capture probability, and constant apparent survival and entry probability.No other model was within two QAICc units of this top-ranking model.Table 1.Summary statistics for primary periods, including survey period, number of survey days, total number of groups sighted, and average group size.

Seasonal and super-population abundance estimates
Seasonal abundance, an estimate of the total number of dolphins using the study area for each season, and superpopulation abundance, representing the total number of dolphins estimated to use the study area between April 2021 and January 2023, were calculated.Seasonal abundance estimates were calculated from the best fitting MSORD model (

Apparent survival and emigration
The rate of apparent survival between seasons from the best fitting MSORD model was 0.95 (± 0.02 SE, 95% CI 0.89-0.98).The probability of a dolphin being a temporary emigrant in primary period t if it was present in the study area in primary period t − 1 ranged from 0.21 (± 0.10 SE) to 0.61 (± 0.8 SE), and the probability of being a temporary emigrant if absent in primary period t − 1 ranged from 0.27 (± 0.1 SE) to 0.91 (± 0.1 SE) (Supplementary Table S2).In all but one instance, the probability of a dolphin being a temporary emigrant from the study area given that it was previously absent ( ψ E→E ) was higher than if it was previously present ( ψ P→E ).

Discussion
This is the first systematic mark-recapture study to assess the abundance and demographic parameters for spinner dolphins off Waiʻanae, Oʻahu.The sampling design was developed based on previous knowledge of the dolphins' behavior and daily movement patterns to estimate abundance, apparent survival, and transition probabilities [22][23][24]49,50,52 . Data colected over two years resulted in the identification of 165 distinct dolphins, many of which were resighted throughout the duration of the study.The most parsimonious MSORD model revealed seasonal variation in abundance that was generally lowest in winter, a high rate of apparent survival, and Markovian emigration.Findings from this study provide up-to-date estimates to inform management and prompt further inquiry into the movement of spinner dolphins around Oʻahu and between neighboring island regions.
The two mark rate estimates (based on D1 and D2 animals) calculated by independent methods in this study are similar (θ 1 = 0.30 ± 0.004 SE, θ 2 = 0.30 ± 0.02 SE), and are within the range of other mark rates reported for coastal spinner dolphin populations in the Hawaiian Islands and elsewhere 49,53,54 .Mark rates for D1 animals ( θ 1 = 0.07 ± 0.002 SE, θ 2 = 0.04 ± 0.01 SE) are lower than those reported for dolphins off the Kona Coast ( θ 1, Kona = 0.35 ± 0.02 SE, θ 2, Kona = 0.36 ± 0.03 SE) 20 .However, an examination of a subset of D1 dorsal fins from the Tyne et al. 20  The rate of apparent survival as estimated by the most parsimonious model was high and constant (0.95 ± 0.02 SE, 95% CI 0.89-0.98)between seasons.This estimate resembles that of spinner dolphins off Kona (0.97 ± 0.05 SE) 20 , however is it important to note that apparent survival in the present study was estimated seasonally instead of annually.High and constant survival is typical for dolphins and other long-lived species with slow reproductive rates 2,55 .This indicates little permanent emigration and low mortality, which are supported by individual www.nature.com/scientificreports/capture histories throughout the study, yet the length of the study (two years) warrants cautious interpretation of long-term survival.Apparent survival is the product of true survival and permanent emigration and reflects true survival if permanent emigration approaches zero.Therefore, the apparent survival rate in this study may represent true survival if the results from two years of study are representative of longer time periods.Seasonal abundance as estimated by the MSORD ranged between a low of 140 individuals (± 36.8SE, 95% CI 84-232) in Winter 2021, to a high of 373 individuals (± 60.0 SE, 95% CI 273-509) in summer 2022.Estimates were generally higher mid-year and lower in winter.The only previously published abundance estimates for spinner dolphins off Waiʻanae fall within this range of abundances 49 , however, it is difficult to evaluate trends in abundance between the earlier efforts and results presented here given differences in assumptions and study designs.
The most parsimonious MSORD model revealed a Markovian pattern of emigration, meaning that an individual's probability of being a temporary emigrant was dependent on whether the individual was an emigrant in the previous primary period.Generally, the probability of being a temporary emigrant during a primary period was higher if the individual was absent from the study area during the previous primary period.The highest transition probability of previous emigrants to the study area, derived as ( 1 − ψ P→E ), occurred between spring and summer 2022, reflecting the highest abundance estimate in summer 2022.Markovian emigration rates suggest that dolphins temporarily emigrate from and return to the study area during later, if not consecutive seasons in a structured movement pattern, however this structure was not determinable from only two years of data and may be further clarified with more years of sampling.The dynamic rates of temporary emigration (Supplementary Table S2) are not opposed with the indication of low permanent emigration suggested by the high apparent survival rate, as permanent emigration implies that dolphins never return to the study area.Information on the sex of dolphins in the population might additionally inform movement patterns, as males and females often exhibit differences in behavior and home range 7 .
Seasonal patterns in abundance and movement are reported for many coastal dolphin populations including Commerson's (Cephalorhynchus commersonii) 56 , Pacific white-sided (Lagenorhynchus obliquidens) 57 , pantropical spotted (Stenella attenuata) 58 , and bottlenose dolphins (Tursiops spp.) 3,59 .These patterns may be influenced by both intrinsic biological and environmental factors.For example, seasonal fluctuations in sea conditions and prey availability coincide with abundance in many delphinid populations, implying temporary emigration to exploit more suitable habitat and foraging conditions 56,60 .Off Bunbury, Australia, social dynamics and mating strategies in bottlenose dolphins drive sex-specific use of certain habitats and suggest that high summer and autumn abundance is linked to seasonal breeding aggregation 7 .In this study, differences between winter and mid-year dolphin abundance may be attributed to environmental variability and/or reproductive seasonality, though more data is needed for definitive conclusions.
The northeasterly trade winds in the Hawaiian Islands weaken between October and April, resulting in fluctuating wind patterns from other cardinal directions, increased rainfall, and bouts of southernly storms 61 .Additionally, during winter, extratropical storms in the North Pacific generate large-amplitude swells that propagate towards Hawai'i 62 .Swell, wind-waves, and runoff from rainfall can increase turbidity in coastal areas 63,64 .Consequently, the Waiʻanae Coast may experience increased turbidity and turbulent sea conditions during winter, while other coastlines around Oʻahu may be more sheltered.As spinner dolphins prefer clear, protected water for resting 65 , they may seek out these alternative coastlines more frequently during winter.This is consistent with results from aerial surveys from Hawaiʻi Island, which revealed a shift in spinner dolphin movement from the Kona Coast to the eastern side of the island during winter, particularly during episodes of southwesterly storms 22 .However, results from these aerial surveys must be interpreted cautiously, as the sample size was small and differences in sighting conditions on the leeward and windward coasts of this island may have influenced abundance estimates.
Seasonal variation in prey distribution might also drive trends in dolphin abundance.As spinner dolphins follow the diel horizontal and vertical migrations of their prey 23 , fluctuations in their abundance may mirror seasonal changes in the spatial distribution of the mesopelagic prey community.Future studies examining seasonal prey distribution and photo-identification of spinner dolphins from other coastlines of Oʻahu 50 may further elucidate the reduced winter abundance of spinner dolphins off Waiʻanae.
Higher mid-year dolphin abundance may be partly explained by seasonality in their reproduction, with a potential influx of transient dolphins for breeding purposes.Patterns of reproduction in delphinids vary widely between species and regional populations, and can result in diffuse or concentrated calving periods 66,67 .While there are few data available on reproductive seasonality for Hawaiian spinner dolphins, inshore Eastern Tropical Pacific (ETP) (Stenella orientalis) spinner dolphins exhibit a calving peak between May and August 66 .Additionally, peaks in hormonal biomarkers such as testosterone and progesterone (indicating ovulation or pregnancy), in males and females, respectively, imply breeding seasonality 68,69 .Hormonal data from three captive Hawaiian spinner dolphins revealed elevated testosterone levels between March and September for one male dolphin, and a sharp increase in progesterone in late summer for two female dolphins 22 .The average gestation period for spinner dolphins is 10-11 months 22 , and evidence suggests higher numbers of neonate dolphins in summer and autumn off Waiʻanae (L.McPherson, personal observations), however neonates have been observed in all seasons.Therefore, it is possible that Hawaiian spinner dolphins have a diffuse peak breeding season mid-year.
Bottlenose dolphins in the vicinity of Bunbury, Australia, exhibit heightened seasonal abundance and an influx of dolphins during a pronounced peak breeding season 3,7 .Similarly, spinner dolphins off Waiʻanae demonstrate increased abundance and sighting frequencies during a potential mid-year breeding season.This period also www.nature.com/scientificreports/witnesses a potential migration of transient dolphins to the study area.In other delphinid species, males possess larger home ranges or display higher dispersal rates compared to females, thereby affording them enhanced mating opportunities 70,71 .Among the 31 unique spinner dolphins observed only once in this study, the majority were sighted during the summer months (n = 13), with only one sighting recorded in winter.As spinner dolphins inhabiting the Oʻahu region are genetically similar with those found in Maui Nui 26 , it is plausible that some level of transience occurs between these two regions.Indeed, movement of spinner dolphins between Hawaiian Islands has been documented, though infrequently 49 .Transient male dolphins from Maui Nui or an offshore population may potentially visit the study area for breeding purposes during the reproductive season.However, the lack of available information regarding the sex of individual dolphins restricts further interpretation of these findings.
The POPAN estimate of super-population size (633 ± 83 SE, 95% CI 491-817) reflects the total estimated number of individual dolphins that used the Waiʻanae Coast between spring 2021 and winter 2023.A comparable estimate of the Hawaiʻi Island stock in 2011 (631, 95% CI 524-761) 20 prompts further inquiry into variability in environmental and anthropogenic factors between the two island regions that might influence dolphin abundance and movement.Despite Tyne et al., (2014)'s suggestion that their 2011 estimate likely represented the entire Hawaiʻi Island stock, it is important to acknowledge that this stock stands out as the most genetically distinct within the Hawaiian Islands, indicating minimal emigration from the island.In contrast, dolphins off Waiʻanae belong to the Oʻahu/4-Islands stock and share genetic similarities with dolphins in the Maui Nui region.Therefore, the super-population estimate in the present study may represent abundance from a broader region than Oʻahu alone, yet additional information on transience and individual movement patterns could provide more insight.
The most recent abundance estimate of the Hawaiʻi Island spinner dolphin stock indicates a possible decline in abundance from previous estimates potentially due to decades of human disturbance 20,35 .Spinner dolphins around Oʻahu face various anthropogenic threats including chemical and noise pollution, harmful interactions with fisheries, and dolphin-centric tourism, yet there is a deficit of information on the population's health and trajectory.Considering the possible declines off Hawai'i Island and the high vulnerability of Oʻahu's spinner dolphins, it is important to establish long-term monitoring efforts to assess population health and inform conservation.
Investigation of the dolphins' around-island movement patterns coupled with additional photo-identification data from other coastlines may prove valuable in determining if population estimates from Waiʻanae are representative of the island-wide population.Given the need for long-term monitoring, these explorations may indicate the viability of Waiʻanae as an indicator site for monitoring spinner dolphins around Oʻahu.Information on the potential transience of dolphins between Oʻahu and Maui Nui may also aid in the interpretation of the super-population size estimate and shed light on total abundance for the Oʻahu/4-Islands stock.

Conclusions
This study provides systematic mark-recapture estimates of abundance and demographic parameters for the highly exposed spinner dolphins off Oʻahu's Waiʻanae Coast and will aid in population monitoring efforts and stock management.The results indicate that (a) abundance estimates vary between seasons, with fewer dolphins using the study area during winter, (b) apparent survival is high and constant, indicating low permanent emigration from the study area, and (c) emigration is dynamic and Markovian.Low abundance of spinner dolphins off Waiʻanae during winter may be due to seasonal environmental conditions that reduce resting habitat quality.High mid-year abundance may indicate a breeding aggregation based on potential reproductive seasonality in Hawaiian spinner dolphins.Further research on the circum-and inter-island movement patterns of individual spinner dolphins may provide insight into total stock size, seasonal trends in abundance and best practices for long term monitoring.

Study area and sampling design
Boat-based surveys were conducted off the Waiʻanae Coast of Oʻahu, Hawaiʻi, departing from either Ko Olina or Waiʻanae marina covering ~ 40 km 2 between Barber's Point (21° 17.5′ N, 158° 06.5 W′) and Kaena Point (21° 34.5′ N, 158° 06.5′), extending 1-km from shore (Fig. 4).Water depth within the study area ranges from < 1 m near the coast to approximately 30 m at 1-km from shore.The deep-water edge off which spinner dolphins nocturnally feed is 2-3 km from shore, where the bathymetry quickly drops off to > 200 m.This area is the preferred habitat for spinner dolphins 65 , and their occurrence in this region is well-described 24 .
Boat-based photo-identification surveys were conducted during two consecutive years (starting in April 2021 and ending in January 2023) with seasonal efforts each winter (January), spring (April), summer (July) and autumn (October) onboard a 7 m research vessel equipped with twin 60hp outboard engines.Surveys were completed on the six best weather days within a season.The survey was designed to achieve complete coverage of the Waiʻanae Coast from the shoreline out to 1-km offshore (Fig. 4).Each survey team consisted of a boat captain and 2-4 visual observers.Acting under the assumption that observers sighted all dolphins within 250 m of the research vessel, two route configurations were trialed during a pilot season in Winter of 2021: a parallelto-shore route and a zigzag transect route.The parallel configuration covered the entire coastline twice, with an inshore and offshore section, at 250 m and 750 m distance from shore, respectively (Fig. 4).The zigzag route was comprised of transect lines out to 1-km across the depth contour, randomly generated for each complete survey of the coastline.Trialing these two different survey configurations allowed a comparison of survey time and sighting effectiveness to optimize the design for future surveys.After the initial pilot season, the parallelto-shore configuration was used for all remaining surveys.

Photo-identification
Spinner dolphin groups were classified according to a 100-m chain rule, where any dolphins within 100 m of each other were considered to be in the same group 72 .During an encounter, two experienced members of the research team used Nikon D500 and Nikon D750 cameras equipped with either a 200 or 400 mm lens to photograph dolphins.Photographers targeted the dolphins' dorsal fins for individual identification 73 , and were instructed to photograph animals randomly, to minimize bias towards distinctive fins.Observations of dolphin behavior and activity state were recorded for each encounter in addition to information about the group's GPS location, current weather conditions, swell height, and sea state.Group size was estimated by observers on the vessel, and via unoccupied aerial system (UAS) when possible.Encounters ended when the team had high confidence for photographic coverage of the group or when weather/sea conditions deteriorated.

Quality and distinctiveness grading of photo-identification images
Images of the spinner dolphins' dorsal fins, which display unique marks and notches, were used to identify individuals 73 .Quantitative quality grading of dorsal fin photographs allowed a selection of images for analysis which minimized misidentification.Following protocols adapted from Rosel et al. 74 , photographs were graded by trained observers (n = 8) on a numeric scale for clarity, contrast, angle and visibility.Photographs were categorized as "excellent", "good" or "poor", the latter of which were excluded from analysis.Good and excellent quality photographs were then graded for feature distinctiveness, as not all fins were sufficiently marked to be included in the mark-recapture analysis.Distinctiveness was scored based on nicks and notches along the trailing and leading edges of the dorsal fin visible from both sides 74 .Highly distinctive fins with features evident in distant and poor-quality photographs were scored as D1, fins with two features or one major feature were scored as D2, fins with very subtle features were scored as D3, and completely clean fins were scored as D4.Photo grading was performed by multiple trained observers, and quality and distinctiveness scores were compared between observers for consistency.

Estimation of the mark rate of the study population
Estimates of abundance in mark-recapture analyses relate only to the identifiable proportion of individuals in the population.To estimate total abundance, estimates are scaled to account for the nondistinctive proportion of the population.We estimated two mark rates following Tyne et al. 20 , by calculating mark rates ( θ 1 and θ 2 ), using distinct (D1 and D2) animals.Mark Rate 1 ( θ 1 , Eq. 1): The first mark rate was calculated with data from all groups of > 20 dolphins in which all animals in the group were photographed at sufficient quality for identification.Mark rate was estimated from the proportion of sufficient quality photographs that contained distinct fins.
(1) θ1 = number of high quality images with distinct fins total number of high quality images with distinct and non distinct fins www.nature.com/scientificreports/Mark Rate 2 ( θ 2 , Eq. 2): The second mark rate was calculated for groups with highly accurate group size estimates, and in which all dolphins in the group were photographed at sufficient quality for identification.This method was applied to photo-identification data from groups of ≤ 20 dolphins under the assumption that group size estimates would be accurate at or below this threshold.
Standard error (SE) for each mark rate was calculated with Eq. ( 3): where n is the sample size in each equation.
To estimate total abundance, an average of the mark rates calculated using method 1 and 2 was used in Eq. ( 4) to adjust the abundance estimate for the proportion of poorly marked and unmarked individuals: where N total is estimated total abundance, N m is the estimated abundance of marked individuals in the popula- tion, and θ is the estimated proportion of distinct individuals.
The standard errors for the total abundace estimate were calculated following the delta method 75 in Eq. ( 5): Log-normal 95% confidence intervals for the total population were calculated with the expression in Eq. ( 6): with a lower limit of N total C and an upper limit of N total × C 76 .

Multi-state open robust design modeling
The sampling approach of this study was specifically designed to follow Pollock's Robust Design (PRD) 41 .An extension of the PRD capture-recapture model, the multi-state open robust design model (MSORD), was then used to estimate dolphin seasonal abundance, apparent survival, and temporary emigration 42,43,45 .The MSORD estimates temporary emigration as transition probabilities ( ψ ) between an observable ( P, present in the study area) and unobservable ( E, temporary emigrant; absent from the study area) state, modelling seasonal movement in and out of the study area (Supplementary Fig. S2).Primary sampling periods (here, seasons) are separated by long time intervals during which the population is assumed to be open.Within each primary period, multiple temporally close secondary sampling periods occur.In classical robust design modelling, the population is assumed closed within primary periods, whereas the MSORD model relaxes this constraint, allowing the population to be open 44,45 .
The MSORD assumes that (1) markings are permanent, unique, and accurately identified, (2) within a sampling occasion, capture probabilities are homogenous among individuals, (3) capture and recapture probabilities are homogenous, (4) the probability of capture for an individual is independent of other individuals, (5)  sampling for secondary periods is instantaneous, (6) survival probabilities are equal between individuals, and (7) individuals may enter and exit the study area once during each primary period 41,45,77 .To minimize violation of assumptions one and two, only individuals with unique and permanent identifying features (D1 and D2) were used for analysis and only high quality ("good" and "excellent") images were graded.Meeting assumptions three and four, capture and recapture probabilities were assumed independent and homogenous, as photo-ID is non-invasive and dolphins were not expected to exhibit behavioral response.Secondary sampling periods were completed in a single day to meet assumption five.Survival probabilities among age-classes may vary, however nearly all well-marked individuals appeared to be adults.Therefore, their survival probabilities between capture periods should be homogenous, minimizing violation of assumption six.It is possible that spinner dolphins entered or exited the study area more than once during a primary period, indicating potential violation of the seventh assumption.However, this is not expected to impact the results, as preliminary data from simultaneous surveys along adjacent coastlines 50 do not show any such movement during secondary periods.
The relationships between key parameters within the sampling structure of the MSORD model are shown in Fig. 5. Capture probability ( p ), the probability of an animal being detected given that it is within the study area, is estimated within primary periods.The probability of capture ( p ) and re-capture ( c ) are assumed equal ( p = c ), as photo-identification methods are non-invasive and should not elicit a "trap response" 1 .Entry probability ( pent ), the probability of entry into the study area during a given secondary period; and persistence probability (2) θ2 = total number of distinct individuals in each group sumof total group sizes , the probability that an animal is within the study area during secondary period j , given that it was available in the area at period j− 1, are also estimated within each primary period.Between primary periods, apparent survival ( S ), which is the product of true survival and fidelity to the study area, i.e., the probability of surviving and remaining within the study area, and transition probabilities to the emigrant state (E) ( ψ P→E ) and ( ψ E→E ) are estimated.Transition probabilities between states sum to 1, therefore transition probabilities to the present state (P) are derived by subtraction (Supplementary Fig. S2).The MSORD also derives number of marked (here, distinctive) animals available in the study area ( N m ), and the average number of secondary periods that an animal stays within the study area during a primary period (residence time), however the latter was not interpreted for the purpose of this study.In the present study, one complete survey of the Waiʻanae Coast represents a secondary sampling period.Surveys were completed in one day to meet the assumption of instantaneous sampling as required by this design.Robust design analyses were carried out using the program MARK 78 .Models were built in which the parameter estimate for apparent survival was held constant S(.) , or allowed to vary between primary periods S(t) .Transition probabilities were modeled with three patterns of emigration: random emigration, ( ψ P→E = ψ E→E ), where the probability of an individual being an emigrant for a given primary period is independent of its absence during the previous primary period, Markovian emigration, ( ψ P→E ≠ ψ E→E ), where the probability of an indi- vidual being an emigrant is dependent on its absence during the previous sampling period, and no emigration ( ψ P→E = ψ E→E = 0 ).Capture probability was held constant p(.) , or allowed to vary with time between primary periods p(season) , or between both primary and secondary periods p(season.survey) .Entry and persistence prob- abilities were also held constant pent(.) ,ϕ(.) , allowed to vary between primary periods pent(season) , ϕ(season) , or between both primary and secondary periods pent(season.day), ϕ(season.day).Models with all combinations of these parameters were tested, and the Akaike Information Criterion with adjustment for small sample sizes (AICc) was used for model selection.All models within two AICc units of the model with the lowest AICc score were averaged if applicable 79 .
There are limited options for assessing parameter identifiability and goodness-of-fit (GOF) in MSORD models.First, data cloning was implemented to affirm that parameters were reliably estimable 80 .Here, the original dataset was cloned × 100 and fed to the suite of MSORD models, after which the standard errors of estimated parameters were examined.For this method, the parameter estimates should not change, but the standard errors for estimable parameters should converge at a rate of 1/r , r being the number of times the dataset is cloned (in this case, 1/100) 80 .Models resulting in parameters with standard errors that did not converge at this rate indicated nonestimable parameters, and these models were excluded from the analysis.To test the underlying model assumptions, a time varying Cormack-Jolly-Seber (CJS) model [81][82][83] was run on each primary period to calculate a global-GOF via average median c , where c is defined as the deviance divided by the number of degrees of freedom.A second test examined GOF by pooling secondary periods such that dolphins were "seen" or "not seen" for each primary period and running a time varying CJS model in MARK's program RELEASE 78 to explore heterogeneity in capture probability (TEST 2 in RELEASE) and survival (TEST 3 in RELEASE).

POPAN modeling
A suite of POPAN models were constructed to estimate the size of the super-population.POPAN models estimate parameters for apparent survival and entry probability in addition to super-population, however, only the superpopulation estimate was interpreted in this study, as parameter estimates for apparent survival and entry probability resulting from the MSORD model are likely more accurate due to its integration of movement dynamics 45,47 .
Captures of spinner dolphins were pooled within field seasons, so that each field season represented one sampling occasion.Capture probability ( p ), apparent survival ( S ), and entry probability ( pent ) were allowed to vary between sampling occasions ( season ) or were held constant ( .).GOF was examined using program RELEASE in MARK, by calculating the average median c for the fully time varying CJS model.As with the MSORD models, model selection was based on AICc score, or QAICc score when adjusted for overdispersion, and models within two AICc or QAICc units of the top-ranking model were explored 79 .

Figure 2 .
Figure 2. Sighting frequency of individual D1 and D2 spinner dolphins photographed between spring 2021 and winter 2023.
catalog revealed a discrepancy in the cut-off between D1 and D2 animals compared to the cut-offs in the present study.Specifically, many fins in the Kona Coast population that were designated as D1s in the Tyne et al. (2014) study, would, by the NOAA PIFSC distinctiveness grading standards, be designated as D2s.Therefore, the mark rates in the present study are likely comparable to Tyne et al. (2014)'s mark rates for D1 animals.

Figure 4 .
Figure 4.The study area covered approximately 40 km 2 of coastline along the Waiʻanae Coast of Oʻahu, extending 1-km from shore between Barber's Point and Kaʻena Point.Black parallel lines represent the survey transect route.This map and the inset of the Main Hawaiian Islands were generated in QGIS (QGIS Development Team, 2024.QGIS Geographic Information System.Open Source Geospatial Foundation Project.http:// qgis.osgeo.org) and Adobe Photoshop (Adobe Inc., 2024.Adobe Photoshop.https:// www.adobe.com/ produ cts/ photo shop.html), respectively.

Figure 5 .
Figure 5. Survey sampling structure modelling the MSORD design, with population parameters in red.Primary periods occur seasonally over the course of two years, each of which contains six secondary sampling periods.Each secondary sampling period represents one complete survey of the Waiʻanae Coast.